Journal of International
Economics 27 (1989) 47-67. North-Nollaid
Jaime de MEL0
Country Economics Department, The World Bank, Washington, D.C. 20433, USA
Sherman ROBINSON*
Department of Agricultural and Resource Economics, University of California, Berkeley, CA, USA
Received July 1986, revised version received November 1988
This paper examines the treatment of exports and imports, and external closure rules, adopted
in recent single-country computable general equilibrium models of small economies. The paper
presents a simple, one-sector analytic model which captures the major features of the multisector counterpart used in applied models. The paper derives graphical and algebraic solutions
to the model and shows that, unlike some earlier external closures, this one gives rise to a wellbehaved, price-taking economy. The model is also useful to illustrate the role of elasticities in
popular trade-theoretic models that include traded and non-traded goods.
1. Introduction
In recent years, two classes of computable general equilibrium (CGE) trade
models have been used to investigate external sector policies: single-country
and multi-country
trade models. The multi-country
trade models [e.g.
halley ( 1985)] have typically been conDeardorff and Stern (1986) and
cerned with resource allocation and welfare implications of tariff reductions
such as those of the Tokyo round. The single-country models have been used
to analyze a variety of external sector issues ranging from the impact of
s, with or without rent
restrictions on foreign trade (e.g. tariffs and
*We thank David Roland-Wolst for help with derivations in the appendix, Taeho Bark, T. N.
Srinivasan for discussions, a referee for very incisive comments, and Gabriel Castillo and
Jackson Magargee for research and logistic support. The World Bank does not accept
responsibility for the views expressed herein which are those of the authors and should not be
attributed to the World Bank or to its affiliated organizations.
0022-1996/89/$3X
t(‘) 1989, Elsevier Science Publishers
48
J. de Melo and S. Robinson, Product dijj’kentiation
seeking) to the impact of changes in net foreign transfers or world prices on
the equilibrium real exchange rate.’
For both types of models, the results from policy simulations depend on
how export and import behavior are modelled. In a recent paper, Whalley
and Yeung (1984) - henceforth WY - examine this issue for single country
models using the term ‘external closure’ to refer to the various assumptions
about export demand and import supply behavior. After noting that most
applied models are quite disaggregated and separate traded and non-traded
goods, they review three external closure rules in single-country models. for
their first closure rule, WY choose a simple two commodity (import and
export) formulation with no non-traded commodity to show that in these
models, ‘. . . there is no currency exchange rate in the conventional use of the
term as a financial magnitude determined from financial sector activity’.’
In the second of their three external closures, WY assert that the
imposition of a zero trade balance condition in a two-good CGE model that
incorporates product differentiation (i.e. the Armington assumption) with
price-taking behavior for imports along with a downward-sloping foreign
export demand curve with constant elasticity yields a model in which both
domestic and foreign offer curves lie on top of one another.3
They are dissatisfied wih this specification and go on to propose a third
external closure: a model with price-taking behavior and no product
differentiation for tradables, plus the inclusion of non-tradables. In essence,
this closure corresponds to a multi-sector version of the well-known dependent economy (Australian) trade-theoretical model. They show that, in this
formulation, there is an exchange rate variable - or ‘parameter’, as they call
it - that measures the relative price between composites of traded and nontraded goods. They show that, in this model, the foreign offer curve is a
straight line, while the domestic offer curve has some elasticity (thereby
following conventional t rade theory). However, they feel that this pricetaking assumption will be unpalatable in empirical models of large countries.
More generally, they note that this model will not allow two-way trade, or
cross hauling, which is widely observed in trade statistics at the aggregation
levels used in all CGE models, and so is not a desirable specification.
‘Dervis, de Melo and Robinson (1982) - henceforth DMR - review the theoretical
specification of single-country trade models and present a number of applications analyzing the
types of issues mentioned above. Robinson (1989) reviews recent models.
‘Whalley and Yeung (1984, p. 126).
‘WY also note that because export and import demand elasticities are not independent, the
reduced forms for the export and import demand functions differ from the specification intended.
Although econometricians do not typically incorporate the restrictions implied by balanced
trade when they estimate export demand and import supply elasticities, the point that trade
balance restrictions should be recognized in specifying combinations of export demand and
import supply elasticities is correct and nicely made. For a general treatment in the ncommodity case see .fones and Berglas (1977).
J. de Meb and S. Robinson, Product dlrerentiation
49
Several points about the WY analysis deserve comment. First, the role of
the exchange rate in computable general equilibrium models has received
attention for some time and we can find no case in which modelers interpret
it as a ‘financial variable’.4 Second, the two-good model with both go&
traded that WY use in their first discussion of external-sector closue does
not represent well any of the applied CGE trade models, which invariably
include some non-traded goods? Third, an external closure using a pricetaking formulation for all tradables in a model with perfect substitution will
be unpalatable for stronger reasons than those mentioned by WY. If the
price-taking formulation is not accompanied by some product differentiation,
the model will generate extreme specialization whenever it is subjected to a
policy simulation such as reduction in tariffs. The assumption of a
downward-sloping foreign demand curve, while it will help (but not fix) the
specialization problem, will lead to unrealistically strong terms-of-trade
effects that will dominate the welfare results of policy changes in singlecountry models!
The essence of the external-sector specification of most recent singlecountry CGE trade models can be captured by a simple one-sector model
with symmetric product differentiation for imports and exports. This model
embodies (and extends) well-understood results from neoclassical trade
theory and provides a compact statement of the external closures found in
most applied models. The model is also useful to illustrate the role of trade
elasticities in the Australian (dependent economy) model with traded and
non-traded goods. We show that the ‘parameter’ referred to by WY in the
analysis of their third external closure still exists in this model. We indicate
how its equilibrium value is influenced by the assumed values for trade
substitution elasticities and by the choice of weights used as a proxy for the
domestic price index in computations of real exchange rate indices.
With this framework, we provide a systematic exploration of the behavior
of a small price-taking economy characterized by product differentiation on
both the export and import sides. We argue that reasons for introducing
product differentiation on the export side are the same as those for
introducing product dif!erentiation on the import side, namely that multisector models, even when they are disaggregated, do not disaggr,-g&e
products sufficiently. This assumption has in fact been used by Dixon et al.
(1982) and by Deardorff and Stern (1986). In Dixon et al. (1982) the
justification is based on producers engaging in joint production, as in the
4See, for instance, DMR (ch. 6, sections 2 and 3j wh Biscxs the rcr!~ nf the real exchange
rate in general equilibrium models.
‘WY do consider in eqs. (22)-(25) a formulation with one domestic good, but only for an
exchange economy. As argued below, this formulation is not a simplified representation of a
typical single-country CGE trade model.
‘See DMR (ch. 6) for a discussion of specialization and chapter 7 for an alternative
specification for export behavior. The empirical importance of terms-of-trade effects with
downward-sloping foreign export demand curves is shown in chapter 9.
50
J. de Melo and S. Robinson, Product d@rentiation
original presentation by owe11and Gruen (1968). While plausible under
certain circumstances, we think that a more general reason along the lines
pointed
out above is the more plausible rationale for introducing symmetric
product differentiation. This said, it should be pointed out [see Anderson
(1985)] that calculations of the costs of protection carried out in aggregate
economy-wide models with product differentiation to overcome the problem
of specialization may severely understate the costs of protection, at least with
respect to partial liberalization. But our purpose here is to study the
properties of economy-wide models, so this issue of bias in results from
applied models can be left aside.
The remainder of the paper is organized as follows. In section 2 we present
the model and use it in section 3 to show how equilibrium is affected by
terms-of-trade shifts and by changes in net capital inflows, both common
experiments in single-country models. The model is also useful for illustrating
the role of elasticities in popular trade-theoretic models that include traded
and non-traded goods. In section 4 we derive an expression for the elasticity
of the domestic offer curve in our model with symmetric product differentiation and set up a numerical example. The expression and the numerical
example show the role of initial conditions (i.e. openness to trade) and of
values of trade substitution elasticities in determining the shape of the wellbehaved domestic offer curve. We also illustrate the well-known fact that once weights entering the relevant price indices are chosen - the equilibrium
value of the real exchange rate (defined as the relative price of traded to nontraded goods) is indeed independent of the choice of numezaire.
el with differentiated trade
For most countries, and especially for developing countries, it is reasonable to assume that the country is ‘small’ on world markets and cannot affect
its international terms of trade. However, it is also reasonable to assume that
world prices in the tradable sectors do not dominate the domestic price
system. We present below a simple analytic model which captures these
stylized facts and discuss its theoretical structure.
We make the following assumptions: (1) domestically produced and
imported goods are imperfect substitutes - the Armtngton assumption; (2)
domestically produced goods sold on the domestic market are imperfect
substitutes for goods sold on the export market; (3) the economy can
purchase or sell unlimited quantities of imports and exports at constant
world prices - the small-country assumption; (4) aggregate production is
fixed; and (5) there is a balance of trade constraint.
2.1.
ode/ equations
s. ( 1) and (2) give t
ation
functions.
J. de Melo and S. Robinson, Product d@rentiation
51
models, and in the numerical example of section 4, eq. (1) is a CES function,
following Armington, and eq. (2) is a CET (constant elasticity of transformation) function.’ For the analysis here, we only require that F( l
) be convex
to the origin, that G( 0) be concave, and that both be homogeneous of degree
one in their arguments. Given the assumption of fixed output, which is
equivalent to assuming full employment, G( 9) represents a production
possibility frontier delineating the tradeoffs between exports and domestic
suPPlY*
Eqs. (3) and (4) translate foreign prices into domestic prices using a
conversion factor, r, which we refer to as the ‘nominal’ exchange rate. It
should be clear, but is worth repeating (as has been pointed out by I3
and WY) that this conversion factor, r, is not a financial exchange rate
variable. Though often referred to as “the’ exchange rate, we refer to it as the
‘nominal’ exchange rate so as not to confuse it with the real exchange rate the relative price of the domestic good in terms of the (fixed) traded goods which is determined by the model. Indeed, the model could be written
without reference to r - as is common in trade theory - by impli
choosing it as numeraire. We use this approach below in subsection
However, since we wish to consider alternative choices of the numeraire, we
maintain r in our formulation!
We assume that producers maximize profits and that demanders minimize
the cost of purchasing a given quantity of composite good Q.’ These
assumptions lead to eqs. (S)-(8). Eqs. (5) and (6) define composite good prices
and are electively dual cost functions. They are homogeneous of degree one
in input prices. Eqs. (7) and (8) give the demand for imports and supply of
exports arising from the first-order conditions.
Since only relative prices matter, the functions describing the model are
homogeneous of degree zero in prices. To set the absolute price level, select r
as numeraire. Eq. (9) gives the equilibrium condition for the balance of trade;
that in foreign units (expressed in terms of the numeraire) the value of
imports equals the value of exports plus B. Finally, eq. (10) is the equilibrium
condition for the supply and demand for the domestic good. (averall, the
model has 10 equations and 10 endogenous variables: Q, M, Dd, D”, E, pm,
Pe, Bd, Pq, and Px. The homogeneity of eqs. (1) and (2) guarantees that the
‘The CET formulation was first suggested by Powell and Gruen (1968). Though more elegant
and easier to work with than the logistic supply curve proposed by DMR, it can be shown that
the two specifications are empirically very close for local changes around equilibrium. De elo
and Robinson (1985) explore analytically in a partial equilibrium context, the imphcations of
product differeRtiatiOR on the domestic price system.
*Under app ro p riate numeraire selection, r becomes the real exchange rate, in which case it
should be referred to as such.
‘In fact for the analysis here, we could assume that eq. (1) is a utility function which
consumers’seek to maximize.
J. de Me10 and S. Robinson, Product di$etentiation
52
Table 1
A one-sector small-country model with differentiated trade.
(1) Q=WWd)
(2)
X=G(E,lq
(3)
pm=riZm
(4)
pe=tie
(5)
P’=fl(P”,Pd)
(6)
p” =g,(pe, p”)
Import aggregation function
Export transformation function
Import price
Export price
Consumer price
Producer price
(7)
$=fWA+)
Import demand equation
(8)
+=&WA
Export supply equation
(9)
ir’“M- Z’E = B
Balance of trade constraint
Domestic demand-supply equilibrium
(10) Dd-V=O
Notes:
M, E = imports, exports
Dd,Ds = demand and supply of the domestic good.
= composite consumer good
Q
R
= composite production
-m = world price of imports
R
-e
K
= world price of exports
r
= conversion factor; ‘nominal’ exchange rate
= domestic price of imports, 44
P”
= domestic price of exports, E
P’
= domestic price of domestic sales, D
Pd
= domestic price of composite consumer good, Q
PQ
= domestic price of composite output, X
PX
B
= exogenous balance of trade, or net foreign capital inflow (or
outflow for negative B)
system satisfies Walras’ Law. This can be easily seen by writing out the
aggregate income and expenditure equations
P”X =I-rB,
total income,
P”x - P”E + PdDs9
the value of production or GDP,
PqQ = P”M + PdDd, total expenditure or absorption.
Given the equilibrium conditions in cqs. (9) and (lo), it follows that income
always equals expenditure. The variable, B, in eq. (9), denominated in foreign
units, can be thought of as representing an increase (or decrease) in real
income measured in terms of imports, given the fixed world price of imports.
2.2. A graphical presendation
his model
is simple enou
erties can be shown
J. de Melo and S. Robinson, Product dlfkrentiation
53
Fig. 1. Equilibrium in the small-country case.
graphically. Fig. 1 presents a four-quadrant diagram that captures the
essential features. For convenience, choose units so that the exogenous world
prices for both exports and imports equal one. Also, set r as numeraire and
initially assume B =O. In this case, the balance-of-trade equation defines the
foreign offer curve and graphs as a 45’ line in quadrant 1. The production
possibility frontier, PP [eq. (2)], is graphed in quadrant
45’ line which simply indicates that domestic go
the domestic market, are available for demand,
CU
domestic goods market. The co
is
consumption possibility frontier,
J. de Melo and S. Robinson, Product dljkrentiation
54
taneously satisfies the balance-of-trade constraint in quadrant 1 and the
possibility frontier in quadrant 4. Given our choice of units and
the assumption that the balance of trade equals zero, the consumption
possibility frontier in quadrant 2 is a mirror image of the production
possibility frontier, PP, in quadrant 4.
In quadrant 2, the import aggregation function, equation 1, generates a
series of ‘iso-good’ curves, II, analogous to indifference curves.po Equilibrium
is achieved at the point of tangency with the consumption possibility frontier.
At this point, the equilibrium price ratios, p”IP” and pdlPe, equal the slope
of the tangents in quadrants 2 and 4, and are derived from the first-order
conditions in eqs. (7) and (8)’ ’ Given our choice of units, the two ratios are
equal, and the equilibrium value of pd is the equilibrium value of the relative
price of non-tradables to tradables. Thus, selecting t as numeraire is
convenient since it allows us to interpret pd as the real exchange rate< In this
model, the foreign offer curve is the 45’ line in the M,E quadrant in fig. 1.
We derive in section 4 the elasticity of the domestic offer curve and show
that it is a well-behaved curve which intersects the straight-line foreign offer
curve.
Consider the limiting ‘Ricardian’ case corresponding to an infinitely elastic
supply of exports. Then PP becomes a straight line, which in turn implies a
straight-line consumption possibility curve. The real exchange rate is now
fixed and, as in a Ricardian world, is determined by technology. Substitution
possibilities in demand only determine the composition of production for
domestic and for export sales.
Our graphical presentation can also be used to consider the closure
criticized by WY; namely, a specification with product differentiation on the
import side and with iess than infinitely elastic foreign export demand. In
this case, the model would include an extra equation, ze = [E/E,] -1’$ where
5 > 1 is the constant price elasticity of foreign export demand and ze is now
endogenous. Now the foreign offer curve is given by:12
production
M =
E;“E”
9
a=l-l/C,
O<a<l,
(2. 1)
which is derived by substituting the above expression for ze into the
balance-of-trade constraint. This case is depicted in fag. 2, where E. is the
equilibrium under the small country assumption (i.e. a= 1). With market
power, the foreign offer curve becomes OC, and the corresponding consumption possibility curve is CoCl with new equilibriuIm at E,. From the diagram,
“If we replace eq. (1) with an explicit utility function, the Go-goods can be interpreted as
indifferencecurves. Nothing changes in the analysis.
* ‘This result can be derived from the maximization of (1) subject to (2) and (9) and is derived
in the appendix.
“Note that for O<[ -c 1, the cx.ternalconstraint slopes downwards.
J. de Me10 and S. Robir-son, Product di$erentiation
Note Foretgn otter cuw dewed under the ossumpton 9 constant foreign demand elostlctty :,I
Fig. 2. Equilibrium with constant foreign demand elasticity.
one can see that assuming market power leads to an optimum with less trade
and a correspondingly lower real exchange rate.
Clearly this model, which is representative of many single-country CGE
models, does not suffer from the problem of overlapping offer curves
described by WY in their discussion of a similar model with constant price
have shown, the
elasticities of foreign demand and import supply.
foreign offer curve in this model has the usual shape.
detail below, the shape of the domestic offer curve
parameters of the export transformation and imp
56
J. de Melo and S. Robinson, Product di$eentiation
and also has the usual shape. Hence the two offer curves will intersect, but
will certainly not coincide.
Is the one-sector model with differentiated trade well behaved?
examine two typical experiments conducted with single-country models: a
terms-of-trade shift and a change in foreign transfers.
3.1. Terms-of-trade change
Fig. 3 shows the effect on equilibrium of an improvement in the terms of
trade (TOT,+ 7?X,) corresponding to an increase in ze, dn” > 0. This
terms-of-trade change shifts out the consumption possibility schedule to
ill the economy supply a larger volume of exports at this improved
COG
terms of trade? The result depends on the shape of the domestic offer curve.
As drawn. in fig. 3, exports fall. The demand for the domestic good increases,
which in turn implies that the domestic offer curve, FF, is inelastic.13 Also
note that the real exchange rate will appreciate. In the limiting ‘Ricardian’
case considered above, the real exchange appreciation will be equal to the
change in terms of trade, i.e. dpd=dSe.
3.2. An increase in foreign transfers
Fig. 4 shows the effect on equilibrium of an increase in foreign transfers
The effect of a transfer, 8, is an upward parallel shift of the external budget
constraint to 0101 and the consumption possibility curve to C,C,. Will the
increase in transfers lead to a real exchange rate appreciation, as one would
expect in a model where the domestic good is consumed? Yes, if the domestic
good is not inferior in consumption, which is the case drawn in fig. 4 and is
guaranteed for the CES function used in practice. Domestic consumption of
D increases, exports fall, and imports rise.
he graphical apparatus developed here can also be used to examine the
effects of a change in commercial policy. This is not done here since it does
not lead to a new insights about the properties of the external closure
under review. e conclude that the specified external closure gives rise to a
well-defined real exchange rate whose variations to policy changes is in
accord with the usual assumptions of neoclassical trade theory for small
nomies. The assu ption of product differentiation thus leads to a much
re realistic small untry model that can accommodate two-way trade
elow that the shape of the domestic offer curve depends on the two substitution
n trade shares.
J. de Melo and S. Robinson, Product differentiation
57
/
/TOT,
/
/
Fig. 3. Terms -of-trade improvement.
and a degree of autonomy in the domestic price system, but retains all the
desirable features of the standard neoclassical model.
.
le
We conclude with a simple numerical example to s
different parameter alues on computed equilibria for a
change. Assuzne, as in typical
and a terms-of-tra
import aggregation function is CE
Then eqs. (1) and (2) in table 1 are
J. de Melo and S. Robinson, Froduct dl@rentiation
Fig. 4. An increase in foreign transfers.
Q=&(/jM-P+(l
-/I?)D-p)-l'p,
CT=&,
X=A,(OfEh+(i --u)D~~,
Q+--,
-
(4.1)
(4.2)
where a bar denotes an exogenous variable and CJand 51 are elasticities of
substitution and transformation, respectively. Following the calibration
common in CGE models, we construct parameters for the CES and CET
J. de Melo and S. Robinson, Product diferentiation
59
Table 2
Base solution values.
Transfer ( fi)
Exports (E)
Imports (M)
Domestic demand (D) GDP (X)
0
25
25
75
100
Table 3
Welfare and real exchange rate calculations for an increase
in transfers.a
s2’
Q
(1)
(2)
(3)
(4)
0.2
0.5
2
5
5
0.2
0.5
2
5
00
106.9
108.7
109.6
109.9
110.0
0.38
0.68
0.91
0.96
1.00
r/P
(5)
0.46
0.75
0.93
0.97
1.00
(6)
0.45
0.74
0.93
0.97
1.00
‘Transfer (B) set equal to 10.
bElasticity of substitution in CES [eq. (l), table 1, and
eq. (4.1)].
‘Elasticity of transformation in CET [eq. (2), table 2,
and eq. (4.2)].
functions to produce the initial equilibrium formulated in table 2 such that
all prices are unity, i.e. n’”= it-e= r = Px = Pm = Pe = 1. l4
Table 3 shows the effects on the welfare indicator, Q (column 3), and on
the real exchange rate (column 4) of setting transfers equal to 10 - i.e. to 10
percent of initial GDP - under different values of the elasticities of import
substitution and export transformation. Note that, in the limit, the increase
in welfare is equal to the transfer itself. This result occurs when the marginal
rate of transformation of production between sales to the domestic and
export markets is infinite, i.e. in the Wicardian case discussed above. As
expected, the required real exchange rate adjustment to absorb the transfer is
an increasing function of the curvature of the CES and CET functions.
In this example, the numeraire is pq=
- 1. Iliad we selected another
numeraire, such as fixing the value of the G P deflator with base year
quantity weights (i.e. to set p”-= l), then the equilibrium values of the
“nominal’ exchange rate (or conversion factor) in column 5 would have been
replaced by the values appearing in column 6. Likewise, with pd= 1 as
numeraire, the equilibrium values for the ‘nominal’ exchange rate would have
been given by the values in column 4. And, with r= 1 as numeraire, the
equilibrium value of pd appearing in column 4 would have corresponded to
14The numeraire is p4= 1 and the solution is found by solving the maximization problem set
in the appendix using the GAMS package developed by Arne Drud and Alex NIeeraus.
J. de Melo and S. Robinson, Product difirentiation
60
the equilibrium value of the real exchange rate. Regardless of the choice of
numeraire, the equilibrium values of the relative price indices appearing in
columns 4 and 6 of table 3 remain unaltered.
In this one-sector model, there is no ambiguity with respect to the
appropriate definition of the real exchange rate, rlpd. In applied work.
however, two problems arise. In multi-sector CGE applications, a choice
must be made with respect to the weights entering the aggregator for the
domestic price index. Even though the choice of weights will affect the
computed values for the equilibrium real exchange rate, the equilibrating
mechanism working through changes in the real exchange rate is the same,
no matter what price is chosen as numeraire.
The other problem relates to the choice of weights used to proxy the
domestic price index in computations of real exchange rate indices. Typically,
the domestic price index is proxied by some published price index such as
the CPI or the GDP deflator, both of which include traded goods. As shown
by the values in the last two columns of table 3, when values of d and Q are
low, the choice of proxy for the domestic price index makes a great deal of
difference in the computed value of the real exchange rate. For example, with
3 = Q =OS, the real exchange rate index with CPI (or GDP) weights used as
proxy has a value of 0.75 (0.74) whereas the correct value is 0.68.
Finally, we come to the shape of the offer curve. It can be shown that the
elasticity of the offer curve, eoc,is given by the following expression?
oc
&
=-
a(0 + a) + no(o +
G&l-o)A
1)
’
(4.3)
where
From expression (4.3), it is clear that the offer curve will be vertical (co”= 00)
for CJ= 1, positively sloping (so’> 1) for c > 1, and negatively sloping (eoc<O)
for a < 11.For given values of Q, &Oc
monotonically decreases for increasing
values of 0 (with discontinuity at Q= 1). For given values of cr, the curvature
of the offer curve is less (8” is lower), the higher is the value uf Q. Finally, for
given values of CJand a, the value of eoc is larger, the more open is the
economy.l 6
Figs. 5(a) and 5(b) trace the elasticity of the domestic offer curve for
different values of 0, B# 1. Negative values of 8” correspond tkj a backwardbending offer curve. In this case, the income effect of an improvement in the
1‘This result is derived in the appendix with ne = 7rrn=1 by choice of units.
‘60penness is defined in the sense of high initial trade (E/D, ki,Ul) shares.
J. de Melo and S. Robinson, Product dlflerentiation
61
Omega(High)=Z.O
m Omega( Low)= 0.2
-40
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
1.4
4.0
1.8
z
SigmaValues
(a)
8
-8
-12
-14
0.2
0.4
0.6
0.8
1
1.2
Sigma Values
Fig. 5. Offer curve elasticity. (a) Medium economy (E,--M,,= 25). Offez curves with high and
low omega. (b) Closed and open economy offer curves, with omega = 1.
J.1.E:-C
62
J. de Mzlo and S. Robinson, Product diflerentiation
terms of trade dominates the substitution effect and less exports are supplied.
Negative values of 4~”imply that the real exchange rate must appreciate to
ensure a greater supply to the domestic market (this is the case drawn in fig.
3). Raising the elasticity of export supply lowers the offer curve elasticity,
which in the limit is unity. This result follows directly from the relation
between the two elasticities along the external budget constraint. Increasing
the degree of openness raises the offer curve elasticity, a result also found in
standard trade-theoretic models.
Finally, fig. 6 traces the equilibrium values obtained from solving the
model with the initial conditions in table 2 under a high and a low set of
trade substitution elasticities. Fig. 6 draws the equilibrium values of the
welfare indicator, the real exchange rate, and the import share in absorption
for different values of the terms of trade. The arrows indicate the path of the
variables as the terms of trade improve. As expected, welfare gains measured
here in terms of absorption, Q, are larger for the higher set of trade
substitution elasticities. The higher gain attributable to greater specialization
appears as a much larger variation in the share of imports in absorption for
the high value of 0. More importantly, fig. 6 confirms the critical role
assumed by the value of CJin determining whether the real exchange rate will
appreciate or depreciate when the terms of trade varies.
The two numeric 1 examples in fig. 6 could be construed to represent a
developing country tiith a low import substitution elasticity and a developed
country with a higher elasticity. For the developing country, adjusting to the
deterioration in its terms of trade requires a real devaluation to generate
increased exports required to pay fcr more expensive crucial imports. For the
developed country, adjustment requires a real revaluation and a decline in
the volume of foreign trade.
In this paper we have studied systematically the typical external closure of
many single-country-applied general equilibrium trade models. We have
shown that the standard assumption of product differentiation on the import
side can be naturally extended to the export side. An external closure with
symmetric product differentiation for imports and exports is theoretically
well behaved and gives rise to normally shaped offer curves. We derive the
elasticity of the domestic offer curve for a one-sector model and illustrate the
model with a numerical example. The numerical example illustrates, under
different trade substitution elasticities, the implications of the choice of
weights used as a proxy for the domestic rice index in computations of real
exchange rate indices. The .model is also u ful to illustrate the role of foreign
trade elasticities in the popular Australian model with traded and no
goods. In particular, we show the crucial role of trade substitution elasticities
J. de Melo and S. Robinson, Product dlrerentiation
63
-
64
J. ;‘z Melo and S. Robinson, Product d@erentiation
on the import side in determining the direction of change of the real
exchange rate for terms-of-trade perturbations.
ix
A.4. Derivation of equilibrium conditions in fig. 1
To show that in equilibrium the MRS in consumption in quadrant 2 is
T in production in quadrant 4, maximize (1) subject to (2)
equal to the
and (9) by setting the following Lagrangian:
L = Q - A,[x - G(E, D)] - Ab[B- fimM + iieE].
(A4
The first-order conditions are:
=o,
aL aQ
~=~+&[7Zm]=0,
From (A.4):
l,=ixg ‘fe.
I
Substitute (AS) into (A.3):
(A*@
J. de Melo and S. Robinson, Product dlgerentiation
65
Choose units so that 2’“=Em- 1. This establishes the condition asserted in
the text, i.e.
P%”
aQ/ao
P=------_
aQ/aM
pm/p’
WaD _ p%”
aG/aE -p’lp”’
(A4
Therefore
Pd Pd
p”l=p”
A.2. Derivation of elasticity of offer curve [eq. (4.3)]”
We proceed in two steps. First, we derive the relation between
and E
when MRS= MRT. In the second step we bring in the balance-of-trade
constraint.
From (4.2) note that the CET defines a relation between E and I), i.e.
l/h
(A.9).
l
1
Using (A.9) in the FOC of the Lagrangian in (A.l) we have:
(A.10)
aL
-=-
aE
aD
aQ
aD aE
Ee
2
b =
(A.11)
0
l
Dividing (A.10) by (A.11) and rearranging gives:
grn-.aQ ae,
aQ _-=
dM
(A.12)
ee aD dE’
The partial derivatives in (A.12) are obtained from differentiation of (4.1),
.
(4.2), and (A.9):
-01Eh
(l-u)
17We thank David Roland-
(1
-W/h
1
E&1*
J. de Melo and S. Robinson, ?roduct d#krentiation
66
Substitution of (A.13), (A.14), and (A.15) into (A.12) yields, after manipulation, the following:
which gives the relation between M and E when MRS=
The second step involves taking into account the balance-of-trade
constraint:
E=gM.
II
(A.17)
Substituting (A.16) into (A.17) and rearranging gives the required equilibrium
relation betwen E and M:
To get an expression for the elasticity of the offer curve, E”‘,note that the
following relationships hold along an offer curve:
1
&OC =,+I,
x
&;+&i= - 1,
(A.19)
where
&oc =-
Log ditYerentiatioraof (A.18) and some algebraic manipulation eventually
yields:
(A.20)
where
J. de Melo and S. Robinson, Product d#erentiation
67
y choice of units let n’”= ii* = 1. Then (A.20) simplifies to:
-5)(1 -a)1
Ei=(cr+a)(a+l)
where
Js
( _ ar)y[“’ 1+ n)l( &I+dl .
Substitution of (A.21) into (A.19) yields eq. (4.3) in the text.
References
Anderson, J., 1985, The inefficiency of quotas: The cheese case, American Economic Review 75,
1, 178-190.
Armington, P., 1969, A theory of demand for products distinguished by place of production,
IMF Staff Papers 16, 159-176.
Deardorlf, A.V. and R.M. Stern, 1986, The Michigan model of world production and trade (MIT
press, Cambridge, MA).
Dervis, K., J. de Melo and S. Robinson, 1982, General equilibrium models for development
policy (Cambridge University Press, Cambridge, England).
Dixon, P. B., B. Parmenter, J. Sutton and D. P. Vincent, 1982, ORANI: A multisector model of
the Australian economy (North-Holland, Amsterdam).
Jones, R.W. and E. Berglas, 1977, Import demand and export supply: An aggregation theorem,
American Economic Review 67, 183-187.
Melo, J. de and S. Robinson, 1985, Product differentiation and trade dependence of the domestic
price system in computable general equilibrium trade models, in: T. Peeters, et al., eds.
International trade and exchange rates, 91-107 (North-Holland, Amsterdam).
Powell, A. and F. Gruen, 1968, The constant elasticity of transformation production frontier and
linear supply system, International Economic Review 9, 315-328.
Robinson, S., 1989, Multisectoral models of developing countries: A survey, in: H.B. Chenery
and T.N. Srinivasan, eds., Handbook of development economics (North-Holland, Amsterdam), forthcoming.
Whalley, J., 1985, Trade liberalization among major world trading areas (MIT Press, Cambridge, MA).
Whalley, J. and B. Yeung, 1984, External sector ‘closing’ rules in applied general equilibrium
models, Journal of International Economics 16, 123-138.